Visualizing data is of vital importance in all aspects of science, commerce, and government. Often results depend on many factors and their interactions.
Experiments are a typical though not the only source of such data. Each experiment in a set of related experiments will share a set of “input” variables or factors and one or more “output” variables. The experimenter has some control over the “input” variables but the system being observed determines how the output variables relate to the inputs.
For example, the inputs to a growing plant system are the nutrients and energy given to the plant such as: carbon level, organic nitrogen level, inorganic nitrogen level, and light level. The output variables might be height of the plant, weight of the plant, or the amount of protein present in the plant after treatment. In this example, the “system” is the growing plant. The system thus determines how the output is related to the input.
Currently, the common visualization method available to show interactions is the Venn diagram. (See FIG. 1). The Venn diagram consists of a collection of either two or three overlapping circles. Suppose there are three circles. Each circle may correspond to an input factor, for example, F1, F2, and F3. The part of the Venn diagram covered by the F1 circle alone corresponds to the experiment when F1 alone is present. The part covered by the F1 and F2 circles but not the F3 circle corresponds to the experiment when F1 and F2. but not F3 are present. The part covered by all three circles corresponds to the experiment when F1, F2, and F3 are present. In short, any combination of F1, F2, and F3 in which at least one is present is captured by some interaction. Thus, a Venn diagram is a visualization tool that can be used for up to three binary variables.
A need exists, therefore, to be able to visually represent the interactions of more than three input factors. This invention answers that need.